The slope of the graph is 100
The slope of 100 means that for each month, Brady's savings increase by $100.
Brady's initial deposit is $300, based on the point (0, 300).
The account balance after 15 Months is $1800
If Brady deposited $500 initially and continued to deposit the same amount each month, the graph will be parallel to the initial graph
This will have a negative slope
The slope means the account balance decreases by $100 each month.
a. Slope of the Graph:
To find the slope (m), you divide the change in y by the change in x:
So, we have
Slope (m) = Change in y / Change in x
Slope = (1500 - 300) / (12 - 0)
Slope = 1200 / 12
Slope = 100
b. Meaning of the Slope:
The slope of 100 means that for each month, Brady's savings increase by $100.
c. Initial Deposit:
Brady's initial deposit is $300, based on the point (0, 300).
d. Account Balance after 15 Months:
With a monthly increase of $100, after 15 months, the total increase is
15 * 100 = $1500.
So, Brady will have $300 + $1500 = $1800 in his account.
e. Depositing $500 Initially and Monthly:
If Brady deposited $500 initially and continued to deposit the same amount each month
The graph would be a line with a slope of $100, starting from $500.
This is represented by the gray line on the attached graph
f. Depositing $300 Initially and Spending in 5 Months:
This is represented by the gray line with a negative slope on the attached graph
g. Why the negative slope
If Brady deposited $300 initially but spent it all in five months, the slope would still be $100, but the negative sign would indicate a decrease.
So, the slope would be -100, meaning the account balance decreases by $100 each month.
Question
The following represents the balance in Brady's savings account.
a. Find the slope of the graph
b. What does the slope represent as a rate of change?
c. How much did Brady deposit when he opened the account?
d. At this rate how much money will Brady have in his account after 15 months. Show your reasoning.
e. If Brady deposited $500 to begin with, but continued to deposit the some amount each month what would this graph look like?
f. If Brady deposited $300 initially, but spent it all in five months show this on the graph?
g. What would the slope of this line be? What does the negative sign indicate?